Emit particles and move particle on this surface
You can achieve this by using Forces to direct the particles to your mesh surface. The key is to change the shape of the field to &quot;Surface&quot; :

Here the cube has a Force Field added, with the type set to Force, Shape of 'Surface' and a negative strength. This will draw all affected particles towards the surface.
Note that particles aren't affected by forces applied to their own mesh - so you need to create a separate mesh to generate the particles. However, this could be in the same location as the mesh - so that it appears that the particles are spawned by the same mesh - if that is a requirement.
I also added a couple of fource fields to affect the particles - a 'Drag' field to slow them down (with Quandratic set to 2.0 to slow fast moving particles more than slow-moving ones) and a Turbulance field to move them about a bit. You could also add a Self Effect force on the particles themselves to push them gently away from each other. You'll need to play with the relative strengths of those forces for your situation but I used -5 for my 'surface' effect, 0.005 for the particle self-effect repulsion force, Linear 1.000 and Quadratic 2.000 for the Drag field and 7.4 for the Turbulence field to give them some 'jiggle'.
I also added Collision to the mesh so as to affect the particles when they do hit the surface - to effectively 'grab' them and slow them a bit - by increasing Stickiness to 0.7, Damping to 1.000 and Friction to 0.25.
This produces the following effect :